Bohr's Model
Atomic Physics The Bohr model shows the atom as a small particle with a positively charged nucleus surrounded by rings of electrons in orbit. Electrostatic forces provided attraction in the rings. Niels Bohr first intro913. The model explained the Rydberg formula for the spectral emission lines of atomic hydrogen. The thoery of the model gave further background information making the experimental Rydberg formula became more solid and was respected more after the Bohr model was introduced. The Bohr model is a primitive model which explains the structure of the hydrogren atom. This model is used to introduce students to quantum mechanics because of its simplicity. The Bohr model is sometimes known as the semiclassical model of the atom. History Before the Bohr model in the early the 20th century, Ernest Rutherford and others had experimented with creating their own models of the atom. What differed greatly from Bohr’s model and the others is that the earlier models consisted of a diffuse cloud around the atom. In this cloud negatively charged electrons surrounded a dense positively charged nucleus. Bohr’s model considered a planetary model for the atom. The electrons, the planets, orbiting around a sun-like nucleus. Although using the planetary model as a guide, it had its flaws. Some charactistics of the atom needed further explantion when using the Bohr Model. For example, the loss of energy by synchrotron radiation. This means that the electrons in orbit must radiate away from its orbit gradually spiralling inwards to the nucleus until the atom was no more. In theory this meant that the atom would be no more instantly, therefore its flaw is that the Bohr model could not explain the atom’s long life. Waves in the Bohr Model In 1924 Louis de Broglie proposed that electrons have a wave nature. He proposed that there was a the relationship between the wavelength of the wave aspect and the mass and speed of its particle aspect. This proposal has been confirmed through several experiments and is one of the fundamental aspects of Quantum Mechanics. When imagining Bohr’s planetary model of the atom think of the orbiting electrons as waves. These waves can be described as standing waves. The electrons move as standing waves in a circular orbit. So in general the circumference equals n times the wavelength, where n is any positive integer. In the above figures the value of n is 1, 2 and 3 respectively. Now we call the integer n the principle quantum number. Note that for the hydrogen atom it completely describes the state of the electron. Waves of the Bohr Model In 1924 Louis de Broglie proposed that electrons have a wave nature. He proposed that there was a the relationship between the wavelength of the wave aspect and the mass and speed of its particle aspect. This proposal has been confirmed through several experiments and is one of the fundamental aspects of Quantum Mechanics. When imagining Bohr’s planetary model of the atom think of the orbiting electrons as waves. These waves can be described as standing waves. The electrons move as standing waves in a circular orbit. So in general the circumference equals n times the wavelength, where n is any positive integer. In the above figures the value of n is 1, 2 and 3 respectively. Now we call the integer n the principle quantum number. Note that for the hydrogen atom it completely describes the state of the electron. Key Ideas • Not every orbit is possible, only those that have discrete quantized energies had orbiting electrons. • Electrons are able to jump from one orbit to another, making the laws of classical mechanics not apply. These electorns have an energy difference supplied by a photon, a single quantum of light. • Orbital angular momentum, L according to the equation - Where n = 1,2,3,… and is called the principal quantum number, and h is Planck's constant. - Technical note: an allowed orbit is one in which the electron mass times its speed times the radius of the orbit is equal to a positive integer n times Planck's constant divided by 2 pi. The integer n can be 1, 2, 3, 17, 108, etc. In fact, there are an infinite number of allowed orbits corresponding to the infinite number of positive integers. - When an electron absorbs energy from incident electromagnetic radiation, it "quantum jumps" into a higher energy allowed state. This higher energy state corresponds to an allowed orbit with a higher value of the integer n. - When an electron is in a higher energy state, it can quantum jump into a lower energy state, one with a smaller value of n, emitting all of its energy as a single photon of electromagnetic energy. - The lowest value of n is 1. - Bohr radius equals the smallest possible radius is 0.0529 - Bohr introduced that electrons orbit in "shells" References • Blaber, Michael 1996 http://wine1.sb.fsu.edu/chm1045/notes/Struct/Bohr/Struct03.htm • Fendt, Walter May 30, 1999 http://www.walter-fendt.de/ph11e/bohrh.htm • Harrison, David M. Department of Physics, University of Toronto 1999 http://www.upscale.utoronto.ca/GeneralInterest/Harrison/BohrModel/BohrModel.html • Dr. Stern, David P May 2005http://www.phy6.org/stargaze/Q5.htm • http://csep10.phys.utk.edu/astr162/lect/light/bohr.html